A368380 Arises from enumeration of a certain class of partial zig-zag knight's paths on the square grid.

0, 0, 0, 1, 0, 5, 1, 20, 8, 75, 44, 275, 208, 1001, 910, 3640, 3808, 13260, 15504, 48450, 62016, 177650, 245157, 653752, 961400, 2414425, 3749460, 8947575, 14567280, 33266625, 56448210, 124062000, 218349120, 463991880, 843621600, 1739969550, 3257112960

Offset: 0

Author

N. J. A. Sloane, Feb 18 2024

Keywords

• nonn

Comments

It would be nice to have a more precise definition.

Links

• Jean-Luc Baril and José L. Ramírez, Knight's paths towards Catalan numbers, Univ. Bourgogne Franche-Comté (2022). Also arXiv:2206.12087 [math.CO], Jan 2023. See Section 3.2.

Crossrefs

Cf. A368378, A368379.

The two bisections are A115144 (shifted, negated) and A115147 (shifted, negated).

Formula

G.f.: (1/x + 1 + 2*R(x) + R(x)^2) * R(x)^3 + R(x)^2 / x = F(x) * R(x), where R(x) = (1 - sqrt(1-4*x^2)) / (2*x^2) - 1 and F(x) is the g.f. of A368379. - Andrei Zabolotskii, Jul 25 2025

Extensions

Terms a(13) and beyond from Andrei Zabolotskii, Jul 25 2025